Achieving volatile potassium promoted ammonia synthesis via mechanochemistry

Potassium oxide (K2O) is used as a promotor in industrial ammonia synthesis, although metallic potassium (K) is better in theory. The reason K2O is used is because metallic K, which volatilizes around 400 °C, separates from the catalyst in the harsh ammonia synthesis conditions of the Haber-Bosch process. To maximize the efficiency of ammonia synthesis, using metallic K with low temperature reaction below 400 °C is prerequisite. Here, we synthesize ammonia using metallic K and Fe as a catalyst via mechanochemical process near ambient conditions (45 °C, 1 bar). The final ammonia concentration reaches as high as 94.5 vol%, which was extraordinarily higher than that of the Haber-Bosch process (25.0 vol%, 450 °C, 200 bar) and our previous work (82.5 vol%, 45 °C, 1 bar).

Study on crystalline grain.
We used the Scherrer equation 1 to estimate the grain size (τ) of the catalyst using equation (1).
is the shape factor, with a typical value of 0.9, is the Cu Kα wavelength (1.5406 Å), is full width at half maximum (FWHM), and is the Bragg angle.
Calculation for bulk N content on each catalyst dependent on XRD measurement.
We also estimated the N concentration of bulk powder for FeKN* and FeN* using the following equations 2,3 .
where, is the diffraction order, ℎ is the distance between the layers, ℎ, , are Miller notations, Fe is the unit cell dimension of the α-Fe (2.8664 Å), Fe,N is the unit cell dimension of the N doped α-Fe and is a conversion constant (0.0099 Å). The unit cell dimensions and the conversion constant of the FeK could be a bit different than that of α-Fe, but as can be seen in the XRD patterns of the 4 samples, they appear to be quite similar to each other. Therefore, we used the same value for all samples.
First, we chose the (110) XRD peak to calculate the ℎ using equation (2). Because the sum of Miller notations (ℎ, , ) is the even number, the should be 1. The Bragg angles of FeKN* and FeN* were 22.15°, and 22.01°, respectively. After determining the ℎ , we calculated Fe,N for FeKN* and FeN* using equation (3). Finally, we used equation (4) to calculate the bulk atomic ratio of the absorbed N on FeKN* and FeN*, which were 2.32 at% and 4.08 at%, respectively.

Calculation for weighted ammonia
The weighted ammonia synthesis rate was calculated with equation (5). We considered both N2 dissociation time and hydrogenation time to calculate the weighted ammonia synthesis rate.
where N 2 is the nitrogen gas adsorption and dissociation rate, H 2 is the hydrogenation rate, N is the nitrogen atom adsorption rate.
Density Functional Theory Calculations for reaction rate constant k and turnover frequency (TOF) The reaction rate constant k is calculated by transition-state (TS) theory 4 , where an activation energy (Ea) is required to overcome the energy barrier of RDS, and k is determined by: where Ea values of the hydrogenation processes are 1.46 eV for FeK and 1.65 eV for Fe, respectively ( Supplementary Fig. 8).
The TOF (in s −1 ) calculation is based on RDS model 5 , which is represented by: where H 2 and NH 3 represent the partial pressures of H2 and NH3, respectively. 1 is the reaction rate constant (a footnote is added for clarity), and K2 is the equilibrium constant of the hydrogenation process (N* + 3 2 H2(g) ⇌ NH3(g) + *), which is calculated by: where ∆ NH 3 is the formation energy of the NH3 molecule, and the values are 0.70 eV for FeK and 0.88 eV for Fe, respectively (Supplementary Fig. 9).
As the initial H 2 is 9 bar according to the experiment conditions, the NH 3 can be represented as      Ref. 7 Ref. 8 Ref. 9 Ref. 10 Ref. 11 Ref. 12 Ref. 13 Ref. 14 Ref. 15 Ref. 16 Ref. 17 Ref. 18 Ref. 19 Ref. 20 Supplementary Fig. 12 | XRD measurements of FeN* and Fe. After nitrogenation, the full width at half maximum became wider, and the peak was shifted to low angle.